History is written by the victors, and they will always exaggerate. More, Shakespeare was writing for the Hollywood of his day, and who would trust Hollywood for historical accuracy? Consider "Pearl Harbor", "Enigma", "A Beautiful Mind", or the worst, "U-571". Each of these is an absolute travesty, defended as "It's only entertainment!"
How can you trust Shakespeare to tell the truth about odds of 5 to 1? Why is it a surprise that it was closer to even?